Yes, because some proprietors would say that it does include that.
Their readers may vote with their feet, as they might well have done in the face of the Milly Dowler revelations, had it come to it, but extreme facts would surely be required. Editors are rarely slow to judge the private lives of others, but those whose privacy is claimed to have been invaded will want to know who is judging, controlling or peer-reviewing the editors. On rare occasions, the civil courts have been asked to do this but the drawbacks here have already been discussed.
Beyond this, the custodians of the press are the PCC but the question has been raised as to whether they have consistently done enough to constitute a break on editorial power.